[GAP Forum] Transitive groups

[mim_ at op.pl]

Hi All,

When using function AllTransitiveGroups I see following
#gap> List(AllTransitiveGroups(DegreeAction,6),G->StructureDescription(G));
[ "C6", "S3", "D12", "A4", "C3 x S3", "C2 x A4", "S4", "S4", "S3 x S3",
  "(C3 x C3) : C4", "C2 x S4", "A5", "(S3 x S3) : C2", "S5", "A6", "S6" ]

This description I understand.

But when I use function TransitiveGroup(n,s) then I see following

   tn:=NrTransitiveGroups(n);
   g:=List([1..tn], s->TransitiveGroup(n,s));
   Print("In dimesion", n, " there are ",tn," transitive groups. \n");
   Print(g, "\n");
   sg:=List(g, x->Size(x));
   Print("Sizes are: ",sg, "\n");

In dimesion6 there are 16 transitive groups. 
[ C(6) = 6 = 3[x]2, D_6(6) = [3]2, D(6) = S(3)[x]2, A_4(6) = [2^2]3, 
  F_18(6) = [3^2]2 = 3 wr 2, 2A_4(6) = [2^3]3 = 2 wr 3, S_4(6d) = [2^2]S(3), 
  S_4(6c) = 1/2[2^3]S(3), F_18(6):2 = [1/2.S(3)^2]2, F_36(6) = 1/2[S(3)^2]2, 
  2S_4(6) = [2^3]S(3) = 2 wr S(3), L(6) = PSL(2,5) = A_5(6), 
  F_36(6):2 = [S(3)^2]2 = S(3) wr 2, L(6):2 = PGL(2,5) = S_5(6), A6, S6 ]
Sizes are: [ 6, 6, 12, 12, 18, 24, 24, 24, 36, 36, 48, 60, 72, 120, 360, 720 ]

Where I can find explanation of the notation A_4(6), F_18(6), in other dimension there are also F(5), E(9), etc. ?

In GAP documentation I cannot find this.

Regards,
Marek Mitros